Clone yourself?
If you want to do both, you find a way. Probably the best option would be to alternate meetings - chapter one week, "big deal club" the next - and arrange to sit down with someone each week to catch up on whichever meeting you didn't attend. Or, if one meeting always runs longer than the other, you go to the shorter meeting, then run off to catch whatever's left of the longer one. Explain to the officers of both orgs, that both are very important to you and that you really want to do both.